Arrow Speed

Formula: Speed (fps) = sqrt((2 * (Draw Weight * Draw Length * Efficiency) / (Arrow Weight * 0.0648)) * 32.174) * 12.0 / 5280 * 3600? Actually, we use: KE = (Draw Weight * Draw Length * Efficiency) / 2? Let's derive: The potential energy stored in the bow is (Draw Weight * Draw Length) / 2? But efficiency reduces it. Then arrow kinetic energy = 0.5 * mass * v^2. So v = sqrt(2 * KE / mass). KE (ft-lb) = (Draw Weight (lbs) * Draw Length (ft) * Efficiency) / 2? Actually, Draw Length in inches, convert to feet. So: KE = (Draw Weight * (Draw Length/12) * Efficiency/100) / 2? Wait, typical formula: speed = sqrt( (2 * (Draw Weight * Draw Length * Efficiency) / (Arrow Weight * 0.0648) ) * 32.174 ) * 12? Let's use standard: Speed (fps) = sqrt( (2 * (Draw Weight * (Draw Length/12) * Efficiency/100) / (Arrow Weight * 0.0648 / 32.174) ) )? Too messy. Let's use simple: Speed (fps) = sqrt( (2 * (Draw Weight * Draw Length * Efficiency/100) / (Arrow Weight * 0.0648) ) ) * 32.174? Actually, we'll implement the common formula: speed = sqrt( (2 * (Draw Weight * (Draw Length/12) * Efficiency/100) / (Arrow Weight * 0.0648) ) * 32.174 ) * 12? No. Let's just use: KE (ft-lb) = (Draw Weight * (Draw Length/12) * Efficiency/100) / 2? Not accurate. Better: Use energy in foot-pounds = (Draw Weight * Draw Length) / (2 * 12) * Efficiency/100? Actually, the potential energy stored in a bow is approximately (Draw Weight * Draw Length) / 2, but Draw Length in inches, so in ft-lb: (Draw Weight * Draw Length/12) / 2 = (Draw Weight * Draw Length) / 24. Then multiply by efficiency. So KE = (Draw Weight * Draw Length / 24) * (Efficiency/100). Then arrow mass in slugs = Arrow Weight grains * 0.000142857? Actually 1 grain = 0.000142857 lb? No, 1 lb = 7000 grains, so mass in lb = Arrow Weight / 7000. Then mass in slugs = mass in lb / 32.174. So v (fps) = sqrt(2 * KE * 32.174 / (Arrow Weight/7000) )? Or simpler: v = sqrt(2 * KE * 32.174 / (Arrow Weight/7000) ). But let's just use: v (fps) = sqrt( (2 * (Draw Weight * Draw Length / 24 * Efficiency/100) * 32.174 ) / (Arrow Weight / 7000) ). Simplify: v = sqrt( (2 * 32.174 * 7000 * Draw Weight * Draw Length * Efficiency) / (24 * 100 * Arrow Weight) ) = sqrt( (450436 * Draw Weight * Draw Length * Efficiency) / (2400 * Arrow Weight) ) = sqrt( (187.6817 * Draw Weight * Draw Length * Efficiency) / Arrow Weight ). So v = sqrt( (187.6817 * Draw Weight * Draw Length * Efficiency) / Arrow Weight ). That's for fps. Then m/s = fps * 0.3048. We'll use this formula.